Recently Submitted Papers
- "Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics." Joint with B. Perthame and M. Doumic.
- "Towards a Generalization of Dupire's Equation for Several Assets."
Joint with P. Amster and P. de Napoli.
Papers Published or Accepted in Refereed Journals
- "Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy." Journal of Mathematical Physics (2008). Joint with L. Fontanelli, P. Lorenzoni and M. Pedroni.
- "Iterative Regularization Methods for a Discrete Inverse Problem in MRI." Cubo. A Mathematical Journal. Vol. 10. N. 8. (2008) pp 135-144. Joint with A. Leitão.
- "On the Inverse Problem for a Size-Structured Population Model." Inverse Problems 23 (2007) pp 1037-1052. Joint
with B. Perthame.
- "Mathematical Modelling and Parameter Estimation of the Serra da Mesa Basin." Mathematical and Computer Modelling (2008). IN PRESS. Joint
with C. Mocenni, E. Sparacino, and A. Vicino.
- "On
the Asymptotics of Fast Mean-Reversion Stochastic Volatility Models."
Joint with M. O. Souza. Accepted for publication in
International Journal of Theoretical and Applied Finance
- "On
the Inverse Doping Profile Problems for the Voltage-Current Map."
Inverse Problems 22 (2006) pp 1071-1088. Joint with A. Leitão and P. Markowich.
- "Huygens'
Principle for Hyperbolic Operators and Integrable Hierarchies."
Physica D. Volume 213, pp. 231-245, (2006). Joint with F. Chalub.
- "Huygens'
Principle, Dirac Operators, and Rational Solutions of the AKNS
Hierarchy." Mathematical Physics, Analysis and Geometry.
Volume 8, Number 3, pp 187-210, (2005). Joint with F.Chalub.
- "Matrix
Bispectrality and Huygens' Principle for Dirac Operators."
Contemporary Mathematics. Vol. 362. pp 89-112, (2004). Joint with
F. Chalub.
- "Three-Dimensional
Reconstruction by Chahine's Method from Electron Microscopic Projections Corrupted by
Instrumental Aberrations." Inverse Problems.
Vol. 19, Number
4, pp 933-950, (2003). Joint with R. Marabini, C.O.S. Sorzano, and G.
T.
Herman.
- "On the
Inverse Problem for Scattering of Electromagnetic Radiation by a
Periodic Structure." Studies in Applied Mathematics. Vol.
111,
Number 2, pp 115--165, (2003). Joint with L. O. Castellano Pérez.
- "On the
Bi-Hamiltonian Theory for the Harry Dym Equation." Theoretical
and Mathematical Physics. Vol. 133, Number 2, pp. 1583--1595,
(2002). Joint with M. Pedroni and V. Sciacca.
- "Bundle
Bispectrality for Matrix Differential Equations." Integral
Equations
and Operator Theory. Vol. 41, pp. 472--496, (2001). Joint with A.
L.
Sakhnovich.
- "Tangent
Graeffe Iteration." Numerische Mathematik. Vol. 89, No. 4,
pp. 749-782 (2001). Joint with G. Malajovich.
- "On the
Geometry of Graeffe Iteration." Journal of Complexity. Vol.
17, No. 3, pp. 541-573 (2001). Joint with G. Malajovich.
- "Convexity
for the Diffuse Tomography Model" Inverse Problems. Vol.
7, pp 729 - 738 (2001). Joint with B.F.Svaiter.
- "On
Huygens' Principle for Dirac Operators and Nonlinear Evolution
Equations." Journal of Nonlinear Mathematical Physics. Vol.
8, Supplement, pp 62-68 (2001). Joint with F. Chalub.
- "A
Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability."Regular
and Chaotic Dynamics. No. 1, Vol. 5, pp 33-52, (2000). Joint with
G. Falqui, F. Magri and M. Pedroni.
- "Rational
Solutions of the Master Symmetries of the KdV Equation"Communications
in Mathematical Physics. Vol. 211, No. 1, pp 85-109, (2000). Joint
with D.S.Valerio Silva.
- "An
Elementary Approach to the Polynomial Tau Functions of the KP Hierarchy
"Theoretical and Mathematical Physics. Vol. 122, No. 1, pp.
23-36, (2000). Joint with G. Falqui, F. Magri and M. Pedroni.
- "Geodesic
Flows on Diffeomorphisms of the Circle, Grassmannians, and the Geometry
of the Periodic KdV Equation."Advances in Theoretical and
Mathematical Physics. Vol. 3, No.4, pp 1027 --1092, (1999). Joint
with M. Schonbek and A. Todorov.
- " Darboux
Transformations, Darboux Coverings, and Rational Reductions of the KP
Hierarchy "Matemática Contemporânea. Vol. 15,
pp 45-65, (1998). Joint with P. Casati, G. Falqui, F. Magri and M.
Pedroni.
- "Bihamiltonian
Formalism and the Darboux-Crum Method . Part I: From the KP to mKP
Hierarchy" Inverse Problems. Vol. 13 No. 3, pp 755-780,
(1997). Joint with F. Magri.
- "On the
Geometry of Darboux Transformations for the KP Hierarchy and Its
Connection with
Discrete KP" Communications in Mathematical Physics. Vol.
188,
No. 2, pp 305-326, (1997). Joint with F. Magri and M. Pedroni.
- "A Fast
and Stable Algorithm for Splitting Polynomials." Computers and
Mathematics with Applications. Vol. 33, No. 3, pp.1-23, (1997).
Joint with G. Malajovich.
- "Rational Solutions of Nonlinear Evolution Equations, Vertex
Operators and Bispectrality." Journal of Differential Equations 97:1,
(1992), 71-98
- "On a Zero Curvature Problem Related to the ZS-AKNS Operator." Journal
of Mathematical Physics, 33:11, (1992), 3666 - 3675.
- "On the Polynomial tau-functions for the KP Hierarchy
and the Bispectral Property." Letters in Mathematical Physics, 24:1,
(1992), 41 - 48.
- "Diffuse Tomography: Computational Aspects of the Isotropic
Case." Inverse Problems, 8:3, (1992), 421-433, Joint
with
F. A. Grünbaum.
- "An Inverse Problem for a Model of Scattered and Diffused
Radiation." F. A. Grünbaum e G. A. Latham. Proceedings of the
Centre for Mathematics and Its Applications, Australian National
University, 31, (1992), 69-81
- "Differential Equations in the Spectral Parameter, Darboux
Transformations and a Hierarchy of Master Symmetries for KdV" Joint
with F. Magri. Communications in Mathematical Physics, 141:2,
(1991), 329 - 351.
- "Image Reconstruction of the Interior of Bodies that Diffuse
Radiation." Science, # 248, (1990), 990-993, J. R. Singer et
al. (click
here for
a list of references to this paper)
- "Differential Equations in the Spectral Parameter for Matrix
Differential Operators." Physica D Nonlinear Phenomena 43:2-3,
(1990), 269-287
Books
- "An Introduction to Inverse Problems; Examples, Methods, and
Questions." Minicourse at the 22nd Brazilian Mathematics
Colloquium. IMPA, 1999.
- " Topics
on Wave Propagation and Huygens' Principle." Minicourse at the 21st
Brazilian Mathematics Colloquium. IMPA, 1997.
Chapters of Books
- "
Inverse Problems for Semiconductors: Models and Methods."
Joint
with A. Leitão and P. Markowich. Inverse Problems for
Semiconductors: Models and Methods.. In: Carlo Cercignani; Ester
Gabetta. (Org.). Transport Phenomena and Kinetic Theory. Applications
to Gases, Semiconductors, Photons, and Biological Systems. Basel:
Birkhauser, 2006.
- "Imaging of Media that Diffuse and Scatter Radiation."
F. A. Grünbaum et al., Radar and Sonar, Part 2, IMA Volumes in
Mathematics and its Applications Volume 39, pp 57-70.
Papers at Conference Proceedings
- "Multiple Scale Asymptotics of Fast Mean Reversion Stochastic Volatility Models." Proceedings of the Third Brazilian
Confererence: on Statistical Modelling in Insurance and Finance.
Sao Paulo : Institute of Mathematics and Statistics, USP. pp. 248-253.
(2007). Joint with M. O. Souza.
- "Asymptotic
Behavior of Stochastic Volatility Models." Proceedings of the Second Brazilian
Confererence: on Statistical Modelling in Insurance and Finance.
Sao Paulo : Institute of Mathematics and Statistics, USP. pp. 222-227.
(2005). Joint with M. O. Souza.
- "Inverse
Problems in Finance: A Short Survey on Calibration Techniques." Proceedings of the Second Brazilian
Conference on Statistical Modelling in Insurance and Finance.
pp. 64-76 (2005).
- "Integrable
Systems, Huygens'
Principle, and Dirac Operators." Proceedings of the Workshop
Nonlinearity,
Integrability and all That. Twenty Years after NEEDS '79 pp 89-96,
(2000).
Joint with F. Chalub.
- " The
Bispectral Problem, Rational Solutions of the Master Symmetry Flows,
and Bihamiltonian Systems" CRM Proc. Lecture Notes, 14,
Amer. Math. Soc., Providence, RI, (1998), 139-155.
- "An
Algorithm for Deinterleaving Pulse Trains Using the Fast Wavelet
Transform" Proceedings of the Brazilian Symposium of
Telecommunications (Recife 1997) Joint with M.A.Grivet, R. Tavora,
and E.L.Pinto.
- "Diffuse Tomography." Joint with F. A. Grünbaum.
"Proceedings of the Meeting on Physiological Imaging, Spectroscopy, and
Early Detection, Los Angeles, Jan. 1993, " SPIE Proceedings, 1887,
(1993),
263-270.
- "Diffuse Tomography." Joint with F. A. Grünbaum et al.
`Proceedings of the Laser Spectroscopy Symposium of the S.P.I.E. Los
Angeles Meeting Jan. 1991." Progress in Biomedical Optics,1431,
(1991), 232-238
- "An Oscillation Theorem for a Hill's Type Equation" Joint with
L. R. Sinay, 17° Seminário Brasileiro de Análise,
(1983), pp 95-100.
Editorial Committees of Books
- Sixth Workshop on Partial Differential Equations. Part II.
Papers from the Workshop on Partial Differential Equations: Theory,
Computation, and Applications held in Rio de Janeiro, July 19--23,
1999. Edited by Hermano Frid, Jorge Hounie, Rafael Iório, Dan
Marchesin, André Nachbin and Jorge Zubelli. Mat. Contemp. {19}
(2000). Sociedade Brasileira de Matemática, Rio de Janeiro,
1999. pp. i--viii and 1--202.
- Sixth Workshop on Partial Differential Equations. Part I.
Papers from the Workshop on Partial Differential Equations:
Theory, Computation, and Applications held in Rio de Janeiro, July
19--23,
1999. Edited by Rafael Iório, Dan Marchesin, André
Nachbin
and Jorge Zubelli. Mat. Contemp. 18 (2000). Sociedade
Brasileira
de Matemática, Rio de Janeiro, 1999. pp. i--viii and
1--207.
- Fifth Workshop on Partial Differential Equations. Papers
from the Workshop on Partial Differential Equations: Theory,
Computation, and Applications held in Rio de Janeiro, July 14--18,
1997. Edited by Paulo Cordaro, Dan Marchesin, André Nachbin and
Jorge P. Zubelli. Mat.
Contemp. 15 (1998). Sociedade Brasileira de
Matemática, Rio de Janeiro, 1998. pp. i--viii and 1--312.
- Fourth Workshop on Partial Differential Equations. Part II.
Papers from the Workshop on Partial Differential Equations: Theory,
Computation, and Applications held in Rio de Janeiro, July 17--21,
1995. Edited by Rafael Iório, Dan Marchesin, André
Nachbin and Jorge Zubelli. Mat. Contemp. 11 (1996). Sociedade
Brasileira de Matemática, Rio de Janeiro, 1996. pp. i--vi
and 1--190.
- Fourth Workshop on Partial Differential Equations. Part I.
Papers from the Workshop on Partial Differential Equations: Theory,
Computation, and Applications held in Rio de Janeiro, July 17--21,
1995. Edited by Rafael Iório, Dan Marchesin, André
Nachbin and Jorge Zubelli. Mat. Contemp. 10 (1996). Sociedade
Brasileira de Matemática, Rio de Janeiro, 1996. pp. i--vi
and 1--180.
General Audience Papers
- "Sólitons:
Na Crista da Onda por mais de 100 Anos." Revista
Matemática Universitária. Vol. 30, pp
44--62, (2001). Joint with F. Chalub.
- "Sólitons:
Na Crista da Onda por mais de 100 Anos." Boletim da Sociedade
Portuguesa Matemática . Vol. 51, pp 3--24, (2004).
Joint with
F. Chalub. Reprinted version of the previous paper.